People are increasingly utilizing portable computing devices, such as smart phones and tablet computers, for a variety of tasks. In many instances, these devices include at least one display screen including a display element, such as a liquid crystal display (LCD) element, at least one touch sensitive component, and an overlying transparent layer. This overlying layer typically comprises a sheet of cover glass, which generally has a uniform thickness to ensure proper connection with various components of the display screen, as well as to prevent unintended optical artifacts. As the size of the display screens increase, and as the thickness of the devices decrease, the transparent cover layers are increasingly subject to damage due to actions such as dropping a device or applying an unexpected point pressure. The edges of the cover layer can be particularly susceptible to damage, which is increasing problematic as the edges of the screen approach the edges of the various computing devices.